There's also the internal manoeuvring to consider for those submitting letters - all those MPs who want Johnson gone don't just want him gone, they want to pick the replacement too. We all know that the most swivel eyed basket case of the final 2 gets the gig via the members' vote, so MPs have to make sure that their choice is in that position.
That's where someone like Tugendhat comes in. He's a Tory MP so of course those who pay attention know he's a dick with an atrocious voting record, but outwardly and in the court of pubic perception he's from the "moderate" end of the party. As an example, those who want Sunak know he can't go up against someone from the "shoot the migrants" school of fash (Truss, Patel) because the populist strain of the membership will go frothy at the thought. They want him up against Tugendhat.
None of them are "waiting and seeing" what Johnson does next, they're all making sure their pick is ready to go.